Over a century ago, Birkhoff [1]} proved that the translation operator is hypercyclic on \(\mathcal {H}({\mathbb {C}})\)  endowed with the compact open topology. Later, MacLane [2]} proved that the differentiation operator is also hypercyclic. These seem to be the first examples of hypercyclic operators. Godefroy and Shapiro
[3]} unified the results of Birkhoff and MacLane by showing that each non-scalar operator \(A\)  (i.e., \(A\ne \lambda I\) ) commuting with \(D\)  is hypercyclic.
